Zidane's Madrid return was confirmed on Monday as he penned a three-year deal to replace Santiago Solari, who had succeeded his initial replacement Julen Lopetegui.
Valverde won only one of his four meetings with Zidane's Madrid last season, though he did manage to dethrone them as La Liga champions.
Asked about his rival's return to the Santiago Bernabeu, Valverde told a media conference: "He's a great manager, he's going to a great club.
"They're going to be our rivals and I look forward to coaching against him."
Their exit was followed by that of Paris Saint-Germain, who squandered a 2-0 first-leg lead against Manchester United, with those results serving as a warning to Barcelona as they face Lyon at Camp Nou in the second leg of a tie level at 0-0.
Barcelona were on the receiving end of a shock loss in last season's competition, going out to Roma with a 3-0 quarter-final second-leg loss having won the first leg 4-1.
Valverde is not concerned with any lingering scars from that humbling, however, adding: "We're not worrying too much about what happened a year ago.
"Last year happened, the other Champions League games are a reminder that there are no small teams and that the result in the first leg doesn't matter much.
"If teams like Real Madird and PSG are going out of the Champions League, that's important. We know PSG are a very big club, and that such big teams have gone out the competition that means we have to be careful."
Ousmane Dembele is a doubt for the visit of Les Gones, with Barca set to make decision after the forward undergoes tests on a hamstring issue.
"First we've got to work out how is he and then we can decide. If he's not OK, clearly he won't be playing," Valverde said.
"It's a decisive game but we're not going to start with one player and then have to bring him off early in the game. We'll make our decision based on [the tests]."